Gaussian Definition and 772 Threads

Gaussian is a general purpose computational chemistry software package initially released in 1970 by John Pople and his research group at Carnegie Mellon University as Gaussian 70. It has been continuously updated since then. The name originates from Pople's use of Gaussian orbitals to speed up molecular electronic structure calculations as opposed to using Slater-type orbitals, a choice made to improve performance on the limited computing capacities of then-current computer hardware for Hartree–Fock calculations. The current version of the program is Gaussian 16. Originally available through the Quantum Chemistry Program Exchange, it was later licensed out of Carnegie Mellon University, and since 1987 has been developed and licensed by Gaussian, Inc.

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  1. Sudharaka

    MHB Gaussian Mixture Models and Geodesics

    Hi everyone, :) This is a question that one of my friends sent me. It is kind of open ended and I don't have any clue about the particular area of research he is undertaking. Therefore I am posting the question here with the hope that anybody knowledgeable in this area would be able to help...
  2. skate_nerd

    MHB Normalization of a gaussian wavefunction

    I'm given a wavefunction (I think it's implied this is some sort of solution to the Schrodinger equation) in my quantum mechanics class, and I need to normalize it to find its constant coefficient. So I have $$\psi(x)=Ne^{-\frac{|x-x_o|}{2a}}$$ And the formula for normalizing this to find \(N\)...
  3. Duderonimous

    Gaussian sphere problem, non uniform charge

    Homework Statement A solid non conducting sphere of radius R=5.60 cm has a nonuniform charge ditribution ρ=(14.1 pC/m^3)r/R, where r is the radial distance from the spheres center. (a) What is the sphere's total charge? What is the magnitude E of the electric field at (b) r=0, (c) r=R/2.00...
  4. Mechatron

    Thermal Noise Frequency & Gaussian Plot

    I want to develop a new model for calculating the frequency of thermal radiation. It is generally accepted that thermal radiation emits white noise with all the frequencies within a certain bandwidth. But when white noise interferes with communication systems, it is carried on what is known as a...
  5. W

    Gaussian Surface Electric Field Problem

    Homework Statement An uncharged spherical thin metallic shell has a point charge q at its center. Find expressions for the electric field Inside the shell Outside the shell has the shell any effect on the field due to q? has the presence of q any effect on the shell? if a second point charge...
  6. koustav

    Gaussian Function: Definition & Relation to Gaussian Distribution

    what is gaussian function?how this is related to gaussian distribution?
  7. koustav

    What is the Gaussian Function? Applications & Derivation

    what is gaussian function?what are it's field of applicaton?how this function is derived,i mean what are the logical reason(approach) behind forming such function?
  8. S

    Solving Gaussian Integral: Stuck on Step

    Hey, I am rather stuck on this gaussian integral... I have come this far, and not sure what to do now: [tex]\int dh_{01}(\frac{h_{01}}{\sigma})^{2}+\frac{\Delta k^{2}(t-x)^{2}h_{01}}{2}-ik_{0}(t-x)h_{01}[\tex] [tex]\int...
  9. A

    Gaussian surface - which charges contribute to the electric field

    Homework Statement in the following figure, the dashed line denotes a Gaussian surface enclosing part of a distribution of four positive charges. a) which charges contribute to the electric field at P? b) is the value of the flux though the surface, calculated using only the...
  10. D

    MATLAB Plotting Gaussian Curves with Matlab

    Matlab rook here, Suppose I'd want to plot the Gaussian for 10 different values for n:function gauss(c,n) = plot_gaussian.m x=-1*c:0.1:c; gauss(x,j)=sqrt(j./pi)*exp(-1*j.*x.^2); for j=1:n plot(x,y) end And then I'll type gauss(3,10) to plot 10 curves in the interval [-3,3] Also, if I'd...
  11. ArcanaNoir

    MHB Finding GCD in Gaussian Integers

    The problem asks to find a generator of the principal ideal <6+7i, 5+3i> in Z[i]. It is my understanding that such a generator must be a greatest common divisor of 6+7i and 5+3i. So, let's call this guy d, we should have d(a+bi)=6+7i and d(c+di)=5+3i. I'm not really sure how to find d. If I...
  12. S

    Complex Analysis - Gaussian Function Integration

    I know that \displaystyle \int_{-\infty}^{\infty}e^{-x^{2}}dx=\sqrt{\pi} (You calculate the square of the integral, combine both integrals, change variable to polar coordinates and you can finally integrate that with ease). But in this exercise I have the following statament: Let be P_{R} the...
  13. K

    MHB Exact inversion of matrix complexity (by Gaussian elimination)

    I would like to check if what I have done is correct. Please, any input is appreciated. **Problem statement:** Consider a non-singular matrix $A_{nxn}$. Construct an algorithm using Gaussian elimination to find $A^{-1}$. Provide the operation counts for this algorithm. **My attempted algorithm...
  14. S

    Archived Gauss Law and the wrong Gaussian surface.

    Homework Statement The problem was to calculate the electric field inside an infinite length cylinder (with radius R) with a non uniform charge density. The charge density depended on r. Its easy enough to solve using a gaussian cylinder with r less than R. But what if I wanted to complicate...
  15. M

    Gaussian integral using integration by parts

    Homework Statement Show in detail that: \sigma_{x}^{2} = \int_{-\infty}^{\infty} (x -\bar{x})^{2} \frac{1}{\sigma \sqrt{2 \pi}}e^{-\frac{(x-X)^{2}}{2\sigma^{2}}} = \sigma^{2} where, G_{X,\sigma}(x) = \frac{1}{\sigma \sqrt{2 \pi}}e^{-\frac{(x-X)^{2}}{2\sigma^{2}}} Homework Equations \int u...
  16. S

    Find the wave function of a Gaussian wave packet

    In particular, i am solving part b. I pulled off a couple of formulas from a textbook, but I'm quite sure they are incorrect to apply here. Can anyone guide me? Below is my attempt.
  17. skate_nerd

    MHB Fourier transform of a gaussian

    I'm given a Gaussian function to apply a Fourier transform to. $$f(x)=\frac{1}{\sqrt{a\sqrt{\pi}}}e^{ik_ox}e^{-\frac{x^2}{2a^2}}$$ Not the most appetizing integral... $$g(k)=\frac{1}{\sqrt{2\pi}}\frac{1}{\sqrt{a\sqrt{\pi}}}\int_{-\infty}^{\infty}e^{ik_ox}e^{-\frac{x^2}{2a^2}}e^{-ikx}dx$$...
  18. L

    Gaussian Integrals for Quantum States of well Defined Momentum

    Consider the Gaussian Integral (eqn 2.64).. is anyone able to explain how the constant of normalization is rationalised?
  19. B

    Gaussian function integral

    Is it possible to obtain a sigma function or Taylor series function for the indefinite integral of a general Gaussian function? If not, why not, and if so, where can I find this infinite series solution? By general Gaussian function I mean f(x) = a \cdot e^{-\frac{(x-b)^2}{2c^2}} + d
  20. fluidistic

    Data analysis , I don't understand why this isn't a Gaussian nor a Ma

    Data "analysis", I don't understand why this isn't a Gaussian nor a Ma I have downloaded all the elo ratings of all active chess players in May of the FIDE and I have made an histogram. I have plotted the result on a graph rating vs number of people with this rating. I do not understand why...
  21. dexterdev

    How to prove that a gaussian rv multiplied by a sine also guassian ?

    How to prove that a gaussian random variable multiplied by a deterministic sinusoid also results in a random variable with gaussian pdf? Suppose here A is a guassian random variable and B is given as below where fc is the frequency of sinusoid and t is the time. B=A∗cos(2π fc t). Is random...
  22. T

    How can I improve my GE program using MATLAB?

    Homework Statement I am writing a GE program and i think i have that correct. I have a matrix and i am trying to find the correct answer. I am not sure where i am going wrong. Homework Equations The Attempt at a Solution %GE with no pivoting function x=ge_nopivot(A,b)...
  23. J

    Gaussian Surfaces and infinite lines of charge

    So I've been wondering.. from my previous post: https://www.physicsforums.com/showthread.php?p=4500082#post4500082 if we have a plane of infinite charge, then electric field does not depend on distance however, for a infinite line of charge: If we use a cylinder with radius 'r' as our...
  24. L

    Gaussian Distrib: What is Standard Deviation of Mean?

    In my course textbook it is written that "approximately 68% of the measurements from a normally distributed set lie within +-1 standard deviation of the mean value". What do they mean by standard deviation of the mean value? They give a definition for "the mean"(of a set of measurements(data))...
  25. J

    Why do Gaussian Surfaces work?

    I was doing a problem: An infinite conducting plane has a uniform surface charge density of 30 μC m‾². Find the electric field strength 7.0 mm from the plane. so we can use a gaussian surface (e.g a cylinder), and come to the conclusion that E = 30 μ / ε but that got me thinking...
  26. S

    Gaussian Integral Simplification

    Homework Statement The integral of (x^n)(e^(-a*x^2)) is easier to evaluate when n is odd. a) Evaluate ∫(x*e^(-a*x^2)*dx) (No computation allowed!) b) Evaluate the indefinite integral of x*e^(-a*x^2), using a simple substitution. c) Evaluate ∫(x*e^(-a*x^2)*dx) [from o to +inf] d)...
  27. E

    What Does Gaussian Smearing Mean in Histograms?

    Hi! I was asked to smear an histogram with a gaussian smearing, but I don't understand what does it mean. Can you please explain me what is a gaussian smearing? Thank you
  28. cqfd

    What is the RMS deviation from the true mean for a Gaussian distribution?

    Hi everyone, I'm new here and this is my first post in this forum. ^^ Homework Statement Suppose that you observe a fluorescent object whose true location is x0. Individual photons come from this object with apparent locations xi in an approximately Gaussian distribution about x0...
  29. W

    Gaussian Surface and Charge Density

    1. A solid dielectric sphere of radius 10 cm has an electric charge uniformly distributed throughout its volume. The electric field at 5 cm from the center of the sphere is 8.6 x 10^4 N/C, pointing radially outward. Calculate the magnitude and direction of the electric field at a point 15 cm...
  30. P

    Is a Gaussian surface truly arbitrary ?

    Consider a point charge q at the vertex of an arbitrary cube. If asked to consider the flux the cube experiences, q/8epsilon seems a natural answer, by constructing seven more such cubes to create an overall cube of 8 times the volume with q at its center. But, this doesn't make sense to me...
  31. S

    Mutual Information between two Gaussian distributions

    Suppose I have a Gaussian probability distribution: N_{A}(0,1). A set of values are generated from this distribution to which an arbitrary amount of Gaussian noise, say N_{B}(0,0.5), is added and then the N_{B} values sorted from lowest to highest. These are then digitised by assigning 0...
  32. J

    Learning Gaussian Integrals for Quantum Mechanics

    Good evening Im starting to learn quantum mechanics from Griffith's book however I am having problems when dealing with Gaussian integrals in the first chapter. What book should I read in order to understand this subject? are there resources about gaussian integrals out there? Thanks a lot.
  33. F

    Maximum Entropy in Gaussian Setting

    Hello, I have a doubt about the distribution of random variables that maximize the differential entropy in a set of inequalities. It is well known that the Normal distribution maximizes the differential entropy. I have the following set of inequalities: T1 < I(V;Y1|U) T2 < I(U;Y2) T3 <...
  34. B

    Gaussian elimination: Proof of correctness

    I have been looking for a proof of correctness of Gaussian elimination, but alas, without much success. Most online resources explain how to apply the algorithm rather than proving correctness. That said, I have been looking for a proof to the following theorem, which is stated in Friedberg's...
  35. I

    Simplifying the Algebra for Gaussian Curvature

    Homework Statement Hello everyone. :) I'm having trouble simplifying the last little bit of this question that deals with Gaussian curvature. I've taken all the required derivatives, and double checked with my professor to make sure that they're correct. I'm only have trouble with reducing...
  36. U

    Integrating Difficult Gaussian Integrals for Multivariate Normal Distributions

    I'm dealing with multivariate normal distributions, and I've run up against an integral I really don't know how to do. Given a random vector \vec x, and a covariance matrix \Sigma, how would you go about evaluating an expectation value of the form G=\int d^{n} x \left(\prod_{i=1}^{n}...
  37. P

    How to choose Gaussian surface

    1 Why do we choose a spherical surface as gaussian surface for a point charge to calculate electric field? In my view, the reason may be i. If we take the point charge at centre, each point of spherical surface will be at same distance from the...
  38. R

    C/C++ [C++] Crank-Nicolson advection of gaussian pulse.

    I tried to used the Crank-Nicolson method to solve the advection equation for a Gaussian pulse using the code on this page and I'm lost at trying to setup the initial values for the Gaussian which is passed as an array into the advection matrix. The Gaussian pulse is defined initial...
  39. C

    Gaussian distribution other than standard form

    what changes does there occur in the result of the gaussian distribution "integration e^-alpha*x^2 dx=sqrt(pi/alpha) if i substitute that x^2 with some (x-a)^2? then what should be the integral result ?
  40. C

    Problems with Gaussian distribution

    Homework Statement consider this Gaussian distribution p(x)=Ae^-(a(x-b)^2) Homework Equations use integration p(x)dx=1 to find out the value of A The Attempt at a Solution hi, i know about the gaussian distribution formula integration e^-alpha*x^2 = sqrt(pi/alpha) now for...
  41. X

    What's the difference between Bell curve and Gaussian distribution

    I was looking to the definition of the Bell curve, and the Gaussian distribution, but I don't see any difference when we represent them in a graph. Both have the same Bell curve. What is the difference between the Bell curve and the Gaussian distribution?
  42. S

    Exponential of Gaussian Distribution

    I'm looking for the expected value of an exponential Gaussian Y=\text{exp}(jX) \text{ where } X\text{~}N(\mu,\sigma^2) From wolframalpha, http://www.wolframalpha.com/input/?i=expected+value+of+exp%28j*x%29+where+x+is+gaussian E[Y]=\text{exp}(j^2\sigma^2/2+j\mu) If I were to use the...
  43. R

    Computing for any general function whose variable is a gaussian

    If I have a variable X whose gaussian distribution is known and let f be a known function, is there a way to compute f(X) (i.e) the resulting gaussian distribution from this? Is the result actually a gaussian distribution?
  44. C

    Quantum Mechanics, a free particle prepared as a gaussian wavepacket

    Homework Statement The problem is given in the attached image. I'm currently trying to work out question one.Homework Equations \phi (k) = \dfrac{1}{2 \pi} \int_{- \infty}^{ \infty} \Psi (x,0) e^{-ikx} dxThe Attempt at a Solution Okay, so the first thing I did was to normalise it, but then I...
  45. F

    Integrating Gaussian integral by parts

    Homework Statement We define I_{n} = \int_{-∞}^{∞}x^{2n}e^{-bx^{2}}dx, where n is a positive integer. Use integration by parts to derive:I_{n}=\frac{2n-1}{2b}I_{n-1} Homework Equations Parts formula. The Attempt at a Solution So I'm just stuck here, I'm baffled and confused. Firstly if I...
  46. M

    CMB Angular Distribution: Understanding Gaussian Random Fields

    Dear all, I don't understand why the Cosmic Microwave Background's angular distribution is considered to to a Gaussian random field initially. The rest of the analysis is roughly clear to me, COBE/WMAP/PLANCK measure the CMB Photons and show the temperature fluctuations w.r.t. the mean...
  47. L

    Path integral and gaussian integral

    I am trying to calculate the functional for real scalar field: W[J] = \int \mathcal{D} \phi \: exp \left[{ \int \frac{d^4 p}{(2 \pi)^4}[ \frac{1}{2} \tilde{\phi}(-p) i (p^2 - m^2 +i \epsilon) \tilde{\phi}(p)} +\tilde{J}(-p) \tilde{\phi}(p)] \right] Using this gaussian formula...
  48. L

    Understanding Gaussian Integral: Question on Hinch's Perturbation Theory Book

    Homework Statement I'm reading Hinch's perturbation theory book, and there's a statement in the derivation: ...\int_z^{\infty}\dfrac{d e^{-t^2}}{t^9}<\dfrac{1}{z^9}\int_z^{\infty}d e^{-t^2}... Why is that true?Homework Equations The Attempt at a Solution Homework Statement Homework Equations...
  49. M

    Gaussian Mixture Model Confusion

    Hi All, I'm trying to implement the Gaussian Mixture Model for background subtraction as described by Chris Stauffer and W.E.L Grimson in their paper "Adaptive background mixture models for real-time tracking." I'm having a little trouble with the logic in the step that updates the mean...
  50. phosgene

    Finding the wave function for a Gaussian wave packet

    Homework Statement Suppose a Gaussian wave packet ψ(x,0) is built out of plane waves according to the amplitude distribution function A_{k} = \frac{Ca}{\sqrt{\pi}}e^{(-a^2(k-k_{0} )^2)} Calculate ψ(x,t) for this packet and describe its evolution. Homework Equations ψ(x,t) =...
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